The town at the center of the border dispute between Ethiopia and Eritrea is Badme.
Badme lies near the western end of the Ethiopia–Eritrea frontier, in a historically contested area associated with Ethiopia’s Tigray region and Eritrea’s Gash-Barka region. Disagreement over the exact colonial boundary and competing administrative claims made the settlement a flashpoint after Eritrea became independent from Ethiopia in 1993.
Fighting began around Badme in May 1998 and grew into the Eritrean–Ethiopian War, which lasted until 2000. The conflict spread beyond the town, involved major battles and air strikes, and caused tens of thousands of deaths and large-scale displacement. A boundary commission later awarded Badme to Eritrea, but implementation remained contentious for years.
A common mix-up is confusing Badme with Asmara or Addis Ababa. Those are national capitals: Asmara is Eritrea’s capital and Addis Ababa is Ethiopia’s. Mekelle is an important city in Ethiopia’s Tigray region, but it is not the disputed border town.